Asymptotic expansion of the solution of a boundary value problem for singularly perturbed integro-differential equations of higher orders


Dauylbayev M. Konisbayeva K.
December 2025Springer Science and Business Media Deutschland GmbH

Boundary Value Problems
2025#2025Issue 1

A boundary value problem for singularly perturbed linear integro-differential equations of higher orders with small parameters at several higher derivatives having the phenomena of initial jumps are considered in this work. This means that starting from a certain order number, the derivatives of the solutions at the initial point tend to infinity as the small parameter tends to zero. Previously, such classes of equations have not been studied. A uniform asymptotic expansion of solutions to the problem under consideration is constructed with an arbitrary degree of accuracy with respect to a small parameter. An estimate of the remainder term of the asymptotic expansion of the solution is proved.

Asymptotic expansion , Boundary layer , Initial jump , Integro-differential equation , Singular perturbation , Small parameter

Text of the article Перейти на текст статьи

Department of mathematics, Al-Farabi Kazakh National University, Al-Farabi 71, Almaty, 050040, Kazakhstan

Department of mathematics

10 лет помогаем публиковать статьи Международный издатель

Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026